Question 1

Rewrite each of the following statements formally.

a) "If the square of an integer is even, then that integer is even."

b) "There exists a prime number such that is even."

Question 2

Prove that given any integer, either it is odd or even.

Question 3

Prove by mathematical induction that 2 + 4 + 8 + 16 + + 2n = 2 + , for all integers 1.